I teach a basic beginners nature photography class at night. "Taking Better Pictures" is always the goal. I do teach f/stop, shutter speed etc.., but what works best is giving them examples of composition.
My first class I always teach them to:
1. Move in closer, 2. Watch Headroom 3. Rule of Thirds. I don't need to tell you about these three but you need to try and communicate it by examples.
I want my students to feel better about just taking better pictures. As their composition improves so does their willingness/eagerness to take it to the next level. The tech stuff and their understanding of it comes later.